In this paper a simple but very general method is given for estimating
a population total with any sampling design when objects in sampled u
nits are observed with imperfect detectability-a problem characteristi
c of many surveys of natural and human populations. In the most genera
l case, the method consists of dividing the value of the variable of i
nterest associated with each detected object by the detection probabil
ity for that object and then proceeding to use the estimation method t
hat would ordinarily be used under the design if there were no detecta
bility problems. Examples illustrating the method include simple rando
m sampling, conventional unequal probability sampling, and adaptive cl
uster sampling.